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The mixed degree of families of lattice polytopes | | Benjamin Nill
; | | Date: |
10 Aug 2017 | | Abstract: | The degree of a lattice polytope is a notion in Ehrhart theory that was
studied quite intensively over the previous years. It is well-known that a
lattice polytope has normalized volume one if and only if its degree is zero.
Recently, Esterov and Gusev gave a complete classification result of families
of $n$ lattice polytopes in $mathbb{R}^n$ whose mixed volume equals one. Here,
we give a reformulation of their result involving the novel notion of a mixed
degree that generalizes the degree similar to how the mixed volume generalizes
the volume. We discuss and motivate this terminology, and explain why it
extends a previous definition of Soprunov. We also remark how a recent
combinatorial result due to Bihan solves a related problem posed by Soprunov. | | Source: | arXiv, 1708.3250 | | Services: | Forum | Review | PDF | Favorites | |
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